# Persi Diaconis

**Persi Warren Diaconis** (/ˌdaɪəˈkoʊnɪs/; born January 31, 1945) is an American mathematician of Greek descent and former professional magician.[2][3] He is the Mary V. Sunseri Professor of Statistics and Mathematics at Stanford University.[4][5]

Persi Diaconis | |
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Persi Diaconis, 2010 | |

Born | |

Nationality | American |

Education | City College of New York (B.S., 1971) Harvard University (M.A., 1972; Ph.D., 1974) |

Known for | Freedman–Diaconis rule |

Scientific career | |

Fields | Mathematics |

Institutions | Harvard University Stanford University |

Doctoral advisor | Dennis Arnold Hejhal Frederick Mosteller[1] |

Doctoral students |

He is particularly known for tackling mathematical problems involving randomness and randomization, such as coin flipping and shuffling playing cards.

## Biography

Diaconis left home at 13[6] to travel with sleight-of-hand legend Dai Vernon, and dropped out of high school, promising himself that he would return one day so that he could learn all of the math necessary to read William Feller's famous two-volume treatise on probability theory, *An Introduction to Probability Theory and Its Applications*. He returned to school (City College of New York for his undergraduate work graduating in 1971 and then a Ph.D. in Mathematical Statistics from Harvard University in 1974), learned to read Feller, and became a mathematical probabilist.[7]

According to Martin Gardner, at school, Diaconis supported himself by playing poker on ships between New York and South America. Gardner recalls that Diaconis had "fantastic second deal and bottom deal".[8]

Diaconis is married to Stanford statistics professor Susan Holmes.[9]

## Career

Diaconis received a MacArthur Fellowship in 1982. In 1990, he published (with Dave Bayer) a paper entitled "Trailing the Dovetail Shuffle to Its Lair"[10] (a term coined by magician Charles Jordan in the early 1900s) which established rigorous results on how many times a deck of playing cards must be riffle shuffled before it can be considered random according to the mathematical measure total variation distance. Diaconis is often cited for the simplified proposition that it takes seven shuffles to randomize a deck. More precisely, Diaconis showed that, in the Gilbert–Shannon–Reeds model of how likely it is that a riffle results in a particular riffle shuffle permutation, it takes 5 riffles before the total variation distance of a 52-card deck begins to drop significantly from the maximum value of 1.0, and 7 riffles before it drops below 0.5 very quickly (a threshold phenomenon), after which it is reduced by a factor of 2 every shuffle. When entropy is viewed as the probabilistic distance, riffle shuffling seems to take less time to mix, and the threshold phenomenon goes away (because the entropy function is subadditive).[11]

Diaconis has coauthored several more recent papers expanding on his 1992 results and relating the problem of shuffling cards to other problems in mathematics. Among other things, they showed that the separation distance of an ordered blackjack deck (that is, aces on top, followed by 2's, followed by 3's, etc.) drops below .5 after 7 shuffles. Separation distance is an upper bound for variation distance.[12][13]

## Recognition

- 1982 – Awarded a MacArthur Fellowship
- 1982 – Awarded the Rollo Davidson Prize
- 1990 – Invited Speaker of the International Congress of Mathematicians (ICM)[14]
- 1995 – Elected to the National Academy of Sciences
- 1997 – Gibbs Lecturer, American Mathematical Society[15]
- 1998 – Plenary Speaker of the ICM[16]
- 2003 – Received an honorary D. Sci. degree from the University of Chicago.[17]
- 2006 – Awarded the Van Wijngaarden Award
- 2012 – Awarded the Levi L. Conant Prize[18]
- 2012 – Fellow of the American Mathematical Society[19]
- 2013 – Received an Honorary Degree from the University of St Andrews.[20]

## Works

The books written or coauthored by Diaconis include:

*Group Representations In Probability And Statistics*(Institute of Mathematical Statistics, 1988)[21]*Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks*(with Ronald L. Graham, Princeton University Press, 2012),[22] winner of the 2013 Euler Book Prize[23]*Ten Great Ideas about Chance*(with Brian Skyrms, Princeton University Press, 2018)[24]

His other publications include:

- "Theories of data analysis: from magical thinking through classical statistics", in Hoaglin, D.C. (ed.) (1985).
*Exploring Data Tables, Trends, and Shapes*. Wiley. ISBN 0-471-09776-4.CS1 maint: extra text: authors list (link) - Diaconis, P. (1978). "Statistical problems in ESP research".
*Science*.**201**(4351): 131–136. Bibcode:1978Sci...201..131D. doi:10.1126/science.663642. PMID 663642.

## References

- Persi Diaconis at the Mathematics Genealogy Project
- Hoffman, J. (2011). "Q&A: The mathemagician".
*Nature*.**478**(7370): 457. Bibcode:2011Natur.478..457H. doi:10.1038/478457a. - Diaconis, Persi; Graham, Ron (2011),
*Magical Mathematics: The Mathematical Ideas that Animate Great Magic Tricks*, Princeton, N.J: Princeton University Press, ISBN 0-691-15164-4 - "Stanford University - Persi Diaconis". Retrieved 2011-10-27.
- "It's no coincidence: Stanford University mathematician and statistician Persi Diaconis will serve as a Patten Lecturer at Indiana University Bloomington". Archived from the original on 2011-11-10. Retrieved 2011-10-27.
- Lifelong debunker takes on arbiter of neutral choices
- Jeffrey R. Young, "The Magical Mind of Persi Diaconis"
*Chronicle of Higher Education*October 16, 2011 - Interview with Martin Gardner,
*Notices of the AMS*, June/July 2005. - O'Conner, J. J.; Robertson, E. F. "Diaconis biography".
*MacTutor*. Retrieved 2 April 2018. - Bayer, Dave; Diaconis, Persi (1992). "Trailing the Dovetail Shuffle to its Lair".
*The Annals of Applied Probability*.**2**(2): 295–313. doi:10.1214/aoap/1177005705. - Trefethen, L. N.; Trefethen, L. M. (2000). "How many shuffles to randomize a deck of cards?".
*Proceedings of the Royal Society of London A*.**456**(2002): 2561–2568. Bibcode:2000RSPSA.456.2561N. doi:10.1098/rspa.2000.0625. - "Shuffling the cards: Math does the trick".
*Science News*. November 7, 2008. Retrieved 14 November 2008.Diaconis and his colleagues are issuing an update. When dealing many gambling games, like blackjack, about four shuffles are enough

- Assaf, S.; Diaconis, P.; Soundararajan, K. (2011). "A rule of thumb for riffle shuffling".
*The Annals of Applied Probability*.**21**(3): 843. arXiv:0908.3462. doi:10.1214/10-AAP701. - Diaconis, Persi (1990). "Applications of group representations to statistical problems".
*Proceedings of the ICM, Kyoto, Japan*. pp. 1037–1048. - Diaconis, Persi (2003). "Patterns in eigenvalues: the 70th Josiah Willard Gibbs lecture".
*Bull. Amer. Math. Soc. (N.S.)*.**40**(2): 155–178. doi:10.1090/s0273-0979-03-00975-3. MR 1962294. - Diaconis, Persi (1998). "From shuffling cards to walking around the building: An introduction to modern Markov chain theory".
*Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. I*. pp. 187–204. - Salsburg, David (2001).
*The lady tasting tea: how statistics revolutionized science in the twentieth century*. New York: W.H. Freeman and CO. ISBN 0-8050-7134-2.. Cf. p.224 - Kehoe, Elaine (2012). "2012 Conant Prize".
*Notices of the American Mathematical Society*.**59**(04): 1. doi:10.1090/noti824. ISSN 0002-9920. - List of Fellows of the American Mathematical Society, retrieved 2012-11-10
- "Archived copy". Archived from the original on 2014-04-07. Retrieved 2014-04-05.CS1 maint: archived copy as title (link)
- Review of
*Group Representations In Probability And Statistics*: - Reviews of
*Magical Mathematics*:- Howls, C. J., "Review",
*Times Higher Education* - Cook, John D. (November 2011), "Review",
*MAA Reviews* - Stone, Alex (December 10, 2011), "Pick a Card, Any Card",
*The Wall Street Journal* - "Review",
*Science News*, December 30, 2011 - Watkins, John J. (2012),
*Mathematical Reviews*, MR 2858033CS1 maint: untitled periodical (link) - Van Osdol, Donovan H. (2012),
*Notices of the American Mathematical Society*,**59**(7): 960–961, doi:10.1090/noti875, MR 2984988CS1 maint: untitled periodical (link) - Benjamin, Arthur (2012),
*SIAM Review*,**54**(3): 609–612, doi:10.1137/120973238, MR 2985718CS1 maint: untitled periodical (link) - Castrillon Lopez, Marco (July 2012), "Review",
*EMS Reviews* - Robert, Christian (April 2013),
*Chance*,**26**(2): 50–51, doi:10.1080/09332480.2013.794620CS1 maint: untitled periodical (link)

- Howls, C. J., "Review",
- Peterson, Ivars (December 12, 2012),
*Magical Mathematics And Topological Barcodes*, Mathematical Association of America - Reviews of
*Ten Great Ideas about Chance*:- Hunacek, Mark (November 2017), "Review",
*MAA Reviews* - Bickel, David R.,
*Mathematical Reviews*, MR 3702017CS1 maint: untitled periodical (link) - Zeilberger, Doron (December 31, 2018),
*Opinion 165* - Hilgert, Joachim (January 2018),
*Mathematische Semesterberichte*,**65**(1): 125–127, doi:10.1007/s00591-018-0217-8CS1 maint: untitled periodical (link) - Bultheel, Adhemar (January 2018), "Review",
*EMS Reviews* - Micu, Alexandru (February 12, 2018), "Review",
*ZME Science* - Dyke, Phil (April 2018), "Review",
*Leonardo* - Case, James (April 2, 2018), "Demystifying Chance: Understanding the Secrets of Probability",
*SIAM News* - Cormick, Craig (April 5, 2018), "Review",
*Cosmos* - Crilly, Tony (June 2018),
*BSHM Bulletin: Journal of the British Society for the History of Mathematics*,**33**(3): 197–199, doi:10.1080/17498430.2018.1478532CS1 maint: untitled periodical (link) - Toller, Owen (October 2018),
*The Mathematical Gazette*,**102**(555): 567–568, doi:10.1017/mag.2018.155CS1 maint: untitled periodical (link) - Cox, Louis Anthony Tony (November 2018),
*Risk Analysis*,**38**(11): 2497–2501, doi:10.1111/risa.13196CS1 maint: untitled periodical (link) - Huber, Mark (2019),
*Notices of the American Mathematical Society*,**66**(6): 917–921, MR 3929582CS1 maint: untitled periodical (link)

- Hunacek, Mark (November 2017), "Review",